Hi, welcome to silkysteps.
Can you speak with your tutor to explain that you're finding it difficult to keep up with research?
In answer,
'normal' refers to a time frame and a pattern, where children's expected stages of development would be reached or achieved.
As an example a child would be expected to begin walking independently from around 10 months old to 18 months - outside of this developmentally 'normal range of time there may be cause for additional support, investigation, celebration. And in the same way the normal range of development would be a pattern of development - which would see a child sit, crawl, pull themselves upright, move around with support of people/walls/furniture on both feet then a step without support, two steps without support, gradually increasing the distance covered, ease of movement, complexity of actions ..
'Normal' has allowance where it recognises each child is individual, unique and where one child will crawl on hands & knees/feet, another will bottom shuffle, another who may have alot of interaction with others may make a transition directly from sitting to walking, another may not walk until 2 years old triggering 'out of the normal range' intervention by agencies and professionals to see what's up/causes of concern ..
This specific section on wikipedia will help you reference back to your Heinemann book -
development milestones and normal range
Ready steady baby,
ready steady toddler,
play talk read are NHS Scotland's pregnancy to 5 programmes, supporting parents in their child's development, they're colourful reads that help look at how wide/narrow the expectations of 'normal are
England's
nhs 0-5 timeline
I hope this helps, best wishes